In this paper, we construct and study a semigroup associated to an action of a countable discrete group on a compact Hausdorff space that can be regarded as a higher dimensional generalization of the type semigroup. We study when this semigroup is almost unperforated. This leads to a new characterization of dynamical comparison and thus answers a question of Kerr and Schafhauser. In addition, this paper suggests a definition of comparison for dynamical systems in which neither the acting group is necessarily amenable nor the action is minimal.

中文翻译：

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广义半群与动态比较

在本文中，我们构造并研究了一个与可数离散群在紧致 Hausdorff 空间上的作用相关的半群，该半群可以看作是半群类型的高维推广。我们研究这个半群何时几乎没有穿孔。这导致了动态比较的新特征，从而回答了 Kerr 和 Schafhauser 的问题。此外，本文提出了一个动态系统比较的定义，在该系统中，作用组不一定适合，作用也不是最小的。